TYPICAL BEAM DIAGRAMS

Deflection, shear, and bending diagrams are shown here for typical beams. The beam with deflection and load diagrams are drawn on top with shear and bending diagrams shown below.  With experience, these diagrams may be drawn by visual inspection prior to computing.  This is useful to verify computations and develop an intuitive sense and visualization regarding shear and bending on beams.  The deflection diagram is drawn, visualizing the deflection of a thin board, flexible ruler, or similar device.  It is drawn grossly exaggerated to be visible.  The shear diagram is drawn at a convenient force scale left to right, starting with zero shear to the left of the beam.  Downward uniform load yields downward sloping shear.  Downward point loads are drawn as downward offset, and upward reactions yield upward offset.  Bending diagrams are drawn, considering the area method; namely, bending at any point is equal to the area of the shear diagram up to that point.  Both, shear and bending must be zero to the right of the right beam end. To satisfy this, requires a certain amount of forward thinking and, in complex cases, even working backward from right to left as well as left to right.

1  Cantilever beam with point load
2  Cantilever beam with uniform load
3  Cantilever beam with mixed load
4  Simple beam with point loads
5  Simple beam with uniform load
6  Simple beam with mixed load
7  Beam with one overhang and point load
8  Beam with one overhang and uniform load
9  Beam with one overhang and mixed load
10  Beam with two overhangs and point loads
11  Beam with two overhangs and uniform load
12  Beam with two overhangs and mixed load